Research Journal of Applied Sciences, Engineering and Technology 11(3): 274-280, 2015
DOI: 10.19026/rjaset.11.1717
ISSN: 2040-7459; e-ISSN: 2040-7467
© 2015 Maxwell Scientific Publication Corp.
Submitted: December 20, 2014
Accepted: March 7, 2015
Published: September 25, 2015
Research Article
Performance of Amplify and Forward Relays with Predicted CSI
1
R. Jeyanthi, 2N. Malmurugan and 1V. Kejalakshmi
K.L.N. College of Engineering, Tamil Nadu 630612,
2
Sri Ranganathan College of Engineering and Tech, Tamil Nadu 641035, India
1
Abstract: In cooperative relay networks, Channel State Information (CSI) is estimated at receiver. The estimated
CSI is sent back to the relays through feedback link. This estimated CSI is often outdated due to feedback delay and
the estimated outdated CSI is used for relay selection and detection which affects the performance of the system.
The outage and error rate performance of the relay selection schemes is highly dependent on the correlation between
the actual channel and their corresponding outdated channel estimates. In this study, the first part of the work
investigates the effect of feedback delay on the outage and error rate performance of Amplify and-Forward (AF)
cooperative relay network. In the second part of the work, actual CSI is predicted using Minimum Mean Square
Error (MMSE) prediction and this predicted CSI is used for relay selection and detection. The best relay selection
and partial relay selection are considered in this study. From the simulation results it is observed that the effect of
correlation coefficient between the actual channel and the corresponding channel estimate is more significant in the
best relay selection than partial relay selection and also the improvement in outage and BER performance are
evident if the actual CSI is predicted.
Keywords: Amplify and Forward (AF) relay, best relay selection, channel prediction, feedback delay, outdated CSI,
partial relay selection, relay selection
in the order of the number of relays by selecting the
relay with the best end-to-end path between the source
and the destination in the case of best relay selection.
However, resource-constrained ad hoc and sensor
networks, monitoring the connectivity of all links can
limit the network lifetime. Such problems have been
mitigated by the development of partial relay selection
schemes, which require channel state information of
either the source-relay links, or the relay-destination
links (Krikidis et al., 2008).
Several concept of relay selection schemes have
been carried out in (Hasna and Alouini, 2003, 2004;
Pabst et al., 2004; Laneman et al., 2004; Bletsas et al.,
2006; Ikki and Ahmed, 2007; Krikidis et al., 2008).
Most of these works deal with the case where perfect
CSI is available for relay selection. Recently in (Vicario
et al., 2009; Torabi and Haccoun, 2010; Suraweera et
al., 2010; Seyfi et al., 2011; Michalopoulos et al., 2012;
Kejalakshmi and Arivazhagan, 2015), the issue of
imperfect CSI was considered. In (Vicario et al., 2009),
the outage probability analysis and the asymptotic
behaviour of DF best relay selection with outdated
channel estimates has been studied and in (Torabi and
Haccoun, 2010), the capacity of AF relay with the
imperfect CSI of the source-relay and relay-destination
channels has been investigated. Further, in (Suraweera
et al., 2010), the effect of feedback delay on the
performance of AF relays with the worst partial
relay selection scheme has been studied. Then, in (Seyfi
INTRODUCTION
Various cooperative relay schemes have been
employed recently in wireless networks and they result
in the performance benefits such as throughput
improvements
and
cellular
signal
coverage
enhancements (Hasna and Alouini, 2003; Hasna and
Alouini, 2004; Pabst et al., 2004). Hence, mobile
broadband communication networks such as 3GPP
LTE-Advanced standards prefer to support relay based
communication. Relays in wireless networks can be
classified as:
•
•
Decode-and-Forward (DF) relays, which decode
and re-encode the information before forwarding it
Amplify and-Forward (AF) relays, which amplify
and forward the signal without hard decoding of
relay selection
The cooperative relays give diversity gain but at
the expense of spectral efficiency since the source and
all the relays must transmit in orthogonal channels
(Laneman et al., 2004). The inefficient utilization of the
channel resources can be minimized by relay selection.
One such scheme is the best relay selection protocol. In
this scheme, a single best relay is selected for data
transmission to the destination. Therefore only two
orthogonal channels are required in this case. In
(Bletsas et al., 2006), a diversity gain has been achieved
Corresponding Author: R. Jeyanthi, K.L.N. College of Engineering, Tamil Nadu 630612, India
This work is licensed under a Creative Commons Attribution 4.0 International License (URL: http://creativecommons.org/licenses/by/4.0/).
274
Res. J. Appl. Sci. Eng. Technol., 11(3): 274-280, 2015
et al., 2011) impact of outdated
channel
state
information due to feedback delay and channel
estimation error on the performance of decode-and
forward relays with the partial relay selection scheme
has been reviewed. In (Michalopoulos et al., 2012),
the impact of outdated CSI on the outage performance
of AF relay selection schemes has been reviewed. Also
in (Bin Zhong et al., 2013), the performance of partial
relay selection has been reviewed with outdated CSI
for Cognitive radio networks. In (Zhang et al., 2014),
the optimization of AF relays has been done with beam
forming by considering the imperfect CSI.
The aim of this study is to predict the actual CSI by
using MMSE prediction to overcome the adverse effect
of outdated CSI due to feedback delay. The predicted
CSI is used for relay selection and detection. The effect
of prediction is reviewed on the outage probability and
error rate for best selection schemes and partial
selection schemes.
Fig. 1: System model
Fig. 2: Training model
channel with training symbols. It is assumed that the
number of training symbols in each frame is sufficiently
lesser than the data symbols so that increasing the
training symbols’ power results in negligible increase in
average power (Fig. 2).
For Relay selection process, the participating relays
send flag packets to the destination, announcing that
they are ready to cooperate. The destination terminal
estimates the downlink CSI in each relay for the entire
path. The Central Unit (CU) receives estimated CSI and
relay selection is made. It feeds back the result of the
relay selection. The relay selections have to be
completed within the channel coherence time.
Otherwise outdated CSI would result in erroneous
selection of relay, causing poor performance in the
system.
Let the estimated channel be ĥ and the old
estimated CSI be ĥ . ĥ and ĥ are related by (Torabi
and Haccoun, 2010):
METHODOLOGY
System model: The cooperative relay setup system
shown in Fig. 1, consists of a single source terminal, S,
number of relays N denoted as Ri, where, i = 1, …, N
and a single destination terminal, D. All relays operate
in the half-duplex AF mode and they use CSI-assisted
variable gain G for amplification. This relaying gain
depends on the instantaneous channel amplitude of the
corresponding S-Ri link. The fading in all S-Ri and Ri-D
paths are assumed to be independent and identically
distributed (i.i.d) with h~СΝ (0, ) There is no direct
S-D link. Hence, S can communicate with D only via
the relay terminals. Let h be the circularlysymmetric
complex Gaussian channel gain between nodes A and
B. Let γ be the instantaneous SNR of link A-B, so
that γ = where N represents the Additive White
Gaussian noise (AWGN) power and it is assumed that
all nodes transmit with unit power.
ĥ = (
Relay selection with outdated CSI:
Channel estimation: There are two phases of
transmission. One is training phase and the other is data
transmission. The training phase takes up a fraction of
the whole block duration. It is assumed that the source
and relay have same transmit power. During the
training phase, the source transmits the known training
sequences to relay. The relay estimates the source relay
link channel using training method.
In this study, block fading scheme is considered.
At the beginning of every block, the first symbols
are assigned for training. Therefore, channel is
estimated once in every T seconds, where T is the
frame duration. The channel realizations are assumed to
be constant over a block and correlated across blocks.
The correlation coefficient between the and
+ ) block is = (2 ) where is the
Doppler frequencyand T is the block duration. At the
beginning of each block, the relay nodes estimate the
!ĥ
ĥ + "1 − %)
(1)
where,
ĥ = The channel which is used for relay selection ℎ' =
ℎ,)* = ĥ
ĥ = The channel used for detection i.e., ℎ = ĥ
The correlation between actual true channel and the
estimated channel is given by = (2 ∆).
where,
= The Doppler frequency
T = The block duration
∆ = Feedback delay, %~СΝ(0, 1)
Best relay selection: Best relay selection is a scheme in
which relay for data transmission is selected by
considering both the S-Ri and Ri-D links. In particular,
it is assumed that the relay with the strongest
275
Res. J. Appl. Sci. Eng. Technol., 11(3): 274-280, 2015
= arg /BC. ,Z. )
“bottleneck” link is selected. Hence, the end-to-end
SNR used by CU for relay selection based on outdated
estimates is given as:
,-. = /01,-2'3 , ,-'3 4 5
(9)
The partial relay selection is done by considering:
= arg /BC. 1,Z2'3 5
(2)
(10)
denotes the estimate of ,67 . The
The selection can also be done with the channel
conditions of the Ri-D links:
= arg /BC. ,-. )
(3)
(11)
= arg /BC. 1,-2'3 5
(4)
where, ,-6789:
;< 9 />
CU activates the relay which satisfies the condition:
= arg /BC. 1,Z'34 5
After relay selection process, the data
communication takes place in two time slots; during the
first time slot the source S transmits the signal to the
relay\] :
Partial relay selection: The selection procedure is
modified accordingly so that only one of the two links
of either the S-Rior the Ri-D path is considered for
partial relay selection. The selected relay is thus
determined by considering S-RiCSI and is given as:
^'_ = "pX h2'_ x + nbc
where, hdbc denotes the S-Rk link, k ∈ [1, Nfchannel
coefficient and nbc , k ∈ [1, Nf denotes the additive
white Gaussian noise component withvariance Ng .
During the second time slot, the selected relay \]
multiplies the received signal by gain G and retransmits
itto D. The received signal at D is given as:
The selection can also be done with the channel
conditions of the Ri-D links:
= arg /BC. 1,-'34 5
(5)
y'_i = "pg hbcj Gybc + nl
= "pg hbcj G1"pX hdbc x + nbc 5 + nl
Relay selection with predicted CSI: To overcome the
effect of feedback delay, the actual CSI is predicted by
an L−tap linear MMSE prediction filter using the past
channel estimates [ĥ(k−∆), ĥ(k−∆ − 1)….ĥ(k−∆ −
L)] as in (Vicario et al., 2009).
The past channel estimates are represented in
vector form h∆ (k) = [ĥ(k−∆),ĥ(k−∆ − 1)….ĥ(k−∆ −
L)] where, ∆ is the feedback delay. Let the predicted
CSI be:
hF(k) = w H h∆ (k)
Due to the CSI-assisted AF mode of operation, the
end-to-end SNR for the selected relay, ,] , = 1,..., N,
can be expressed as in (Pabst et al., 2004):
,] =
where, w is the prediction filter coefficients and is
given as:
w=R p
(7)
R = E{h∆ (k)h∆ k)M }is the correlation matrix and p
= E{h(k)h∆ (k)} is the cross correlation vector:
The correlation coefficient NOP =Q
R
RS
STU
V
;< 9 />
cj
cj
sK
(14)
Hence, in this section, the outage probability for
the best relay selection and partial relay selection with
prediction is derived. The outage probability is defined
as the probability that drops below a predefined SNR
threshold. Therefore, to derive the outage probability
for the best relay selection scheme with channel
prediction, the CDF to_ ,) is given as:
where, pX is the power of source and Y is noise
variance.
After prediction at receiver, the relay selection has
been done by CU with predicted CSI. Hence ℎ' =
ℎ,)* = ℎF and ℎ = ℎF. The best relay selection is
determined by:
where, ,Z6789[
opq_ or
opq_ sor
PERFORMANCE ANALYSIS
pH RJK p
,Z. = /01,Z2'3 , ,Z'3 4 5
(13)
where,
hbcj = The channel coefficient of the selected relay
link R m − D
nl = The AWGN component at D with variance NU
(6)
JK
(12)
to_ ,u ) = vw x
=
(8)
denotes the predicted ,67 . The CU
opq_ oq_ i
< ,u z
opq_ soq_ i sK
o
|
∞
pq_
< ,u z oq i ^)}^
{ vw xo s|sK
_
pq_
(15)
And ,2'_ and ,-2'_ are correlated exponential
distributions given by (Pabst et al., 2004):
activates the relay which satisfies the condition:
276
Res. J. Appl. Sci. Eng. Technol., 11(3): 274-280, 2015
opq
~
o
_ , pq_
€T

‹ pq
‚ƒ„
‰Š
ƒ,…†‡ˆ
P
C, ^) =
‹pq
‚KJ ƒ,…†‡ˆ
‰o
Œ 
Q ƒ,…†‡ˆ
Ž|

‹pq
‚KJ ƒ,…†‡ˆ
‰o
(16)
The conditional PDF is given as:
opq
~
o
_ pq_
C
^) =
And substitute:
o~pq (^) = ‹
K
opq
~
o
_ pq_
~ pq
pq ,Š
Š
~
pq
Ž,|)
|)
(17)
‘J ‹
|
opq
Hence,
opq
Š
C
^) =
(18)
€T„
ƒ,…†‡ˆ 

‹ pq
‚ƒ„
‰Š
ƒ,…†‡ˆ
P
‹pq
‚KJ ƒ,…†‡ˆ
‰o
Œ 
Q ƒ,…†‡ˆ
Ž|

‹pq
‚KJ ƒ,…†‡ˆ
‰o
(19)
obtained as in (Pabst et al., 2004) and it is shown in Eq. (20). In equation (20), NOP =Q
pH RJK p is the
Using the above equation, the outage probability for the best relay selection scheme with channel prediction is
RS
RSTU
V
prediction coefficient.
Similarly, the outage probability for partial relay selection scheme with channel prediction is obtained as in
(Pabst et al., 2004) and it is shown in Eq. (21) and in Eq. (21), K,NOP =Q
of S-\] link:
to_ ,u ) = ’>JK
Y8
Š–
VTƒ)Š– „…†‡ˆ ‹

VTƒ)‡ Š
•
‹ p‚ƒ,ƒ,V,„…†‡ˆ ‰
Š
>”YsKsYP
“
Š–
ƒ
‹ šJK)VTƒ ‚›ƒ‰œ YsK)YsK)
PŠ
V
™
˜
—
>JK
+ ’>JK
Y8 ’ž8
RS
RSTU
V
pH RJK p is the prediction coefficient
›ƒ
> JK)VTTƒ YsK)ƒ ‚›ƒ
V ‰‚  ‰
‹ žsK)YsK)21K,K,ž, …†‡ˆ 5
o
Ÿ
(20)
t ] (,u )= 1 − 2 ¢
Ÿ ‘C§ ¨−
>JK
£−1)¤ 1>JK
5¥ × Q
ž
‹
o
ž8
‹qi so
‹pq sž‚o
‹qi so
‹pq Jo
‹pq ƒ,…†‡ˆ
šo
‰œo–
‹pq o
‹qi šKsž‚KJ ƒ,…†‡ˆ
o
‰œ
o– o– sK)
žsK)šKsž‚KJ
‹
o
qi pq
ƒ,…†‡ˆ ‰œ
© × KK ¨2Q
277
žsK)o– o– sK)
©
‹pq o
‹qi šKsž‚KJ ƒ,…†‡ˆ
o
‰œ
(21)
Res. J. Appl. Sci. Eng. Technol., 11(3): 274-280, 2015
SIMULATION RESULTS AND DISCUSSION
The computer simulations are done with using
MATLAB 7.7. The number of relays used in this study
is considered to be 3 and all participating links are
assumed to be symmetrical so that ,«2'_ = ,«'_ 4 i = 1,
2, 3.
Figure 3 describes the outage probability
performance of the best relay selection scheme of AF
relays against the normalized average SNR of S-\] and
R-¬] links for various values of correlation coefficients
with prediction and without prediction. The outage
performance for perfect CSI is also shown in the figure
for comparison.
It is observed that there is a gap between the outage
curves for ρ = 1 and ρ = 0.95 resulting with a small
deviation in the feedback delay (ρ = 0.95) from perfect
CSI (ρ = 1), there is a large degradation in the outage
performance. Even there is a small feedback delay, the
performance degradation is significant. This outage
degradation can be compensated by predicting the
channel using MMSE predictor. The prediction length
is assumed to be L = 6. The curve which corresponds to
the channel prediction with ρ = 0.95 shows better
performance than the curve which corresponds to ρ =
0.95 without prediction. Channel prediction on the
other hand, improves the correlation between the actual
channel values and the CSI available for relay selection
i.e., NOP >. Therefore, the degradations due to
channel variations are reduced. Thus, with the channel
prediction at the receiver, when the correlation
coefficient is ρ = 0.95 the SNR gain of 1dB is
obtained. The outage curves correspond to correlation
coefficient ρ = 0.5 and ρ = 0.707 with prediction and
without prediction show nearby performance. Hence, it
is observed that when feedback delay is high; channel
prediction does not improve the outage performance. It
is also noted that the set of outage curves which
corresponds to ρ = 0.95 shows better outage
performance than the curves corresponds to ρ = 0.5 and
ρ = 0.707.
Figure 4 shows the outage performance of partial
relay selection for various values of correlation
coefficient with and without channel prediction. In this
scheme, outage performance degradation is less
affected by feedback delay. This is due to the partial
channel knowledge either S-\. or R-¬. link used for
selection. The set of outage curves which corresponds
to ρ = 0.5 and ρ = 0.707 have nearby performance.
The curve which corresponds to the channel prediction
with ρ = 0.95 gives SNR gain of 0.5dB than the curve
which corresponds to ρ= 0.95 without prediction.
Figure 5 describes the BER performance of best
relay selection against average normalized SNR for
various values of frame delay with and without channel
prediction. The BPSK modulated symbols are used for
this simulation. The set of error rate curves which
Outage probability
10
Without prediction rho = 0.5
With prediction rho = 0.5
Without prediction rho = 0.707
With prediction rho = 0.707
Without prediction rho = 0.95
With prediction rho = 0.95
Perfect CSI, roh = 1
3
-1
10
10
10
-2
-3
10
-4
0
5
10
15
20
Average normalized SNR in dB
25
Fig. 3: Outage performance of best relay selection
Outage probability
10
10
10
Without prediction rho = 0.5
With prediction rho = 0.5
Without prediction rho = 0.707
With prediction rho = 0.707
Without prediction rho = 0.95
With prediction rho = 0.95
Perfect CSI, roh = 1
0
-1
-2
10
-3
0
10
15
20
5
Average normalized SNR in dB
Fig. 4: Outage performance of partial relay selection
278
25
corresponds to ρ = 0.5 and ρ = 0.707 shows nearby
performance. The set of curve which corresponds to
ρ = 0.95 has better BER performance than the curves
which corresponds to ρ = 0.5 and ρ = 0.707. When no
frame delay is supposed to be ρ = 1 and the small
deviation at ρ = 0.95 results with degradation in the
error rate performance. The curve which corresponds to
channel prediction (prediction length L = 6) with
ρ = 0.95 results in SNR gain of 1 dB than the curve
with ρ = 0.95 without channel prediction.
Figure 6 describes the BER performance of partial
relay selection against average normalized SNR. The
error rate performance is less affected by the CSI
imperfections in partial relay scheme. The outage
curves which correspond to ρ = 0.5, ρ = 0.707 and
ρ = 0.95 show nearby performance. The curve which
corresponds to the channel prediction with ρ = 0.95
Res. J. Appl. Sci. Eng. Technol., 11(3): 274-280, 2015
10
Bit error rate
10
10
0
-1
-2
10
-3
10
-4
10
10
The dependence of correlation coefficient on delay
and prediction length is shown in Fig. 7. The
correlation increases with filter length. For delay of
1msec the maximum value of ρ = 0.97 whereas for a
delay of 3 m sec, the maximum ρ = 0.85. When delay
increases, the inputs to the channel predictor are less
correlated with the actual channel. Hence, there is
degradation in the prediction performance.
Without prediction rho = 0.5
With prediction rho = 0.5
Without prediction rho = 0.707
With prediction rho = 0.707
Without prediction rho = 0.95
With prediction rho = 0.95
Perfect CSI, roh = 1
CONCLUSION
The effects of outdated channel estimates of
amplify and forward best relay selection and partial
relay selection schemes on outage and error rate
performance has been analysed. Simulation results out
of these analysis show that performance degradation is
significant even if it deviates slightly from the perfect
value (ρ = 1), ρ = 0.95 and this degradation effect has
been minimized by MMSE prediction adopted in this
study. This channel prediction results with SNR gain of
1dB in case of best relay selection scheme and 0.5dB in
case of partial relay selection scheme proposed in this
study.
-5
-6
0
10
15
20
5
Average normalized SNR in dB
25
Fig. 5: BER performance of best relay selection
Bit error rate
10
10
10
Without prediction rho = 0.5
With prediction rho = 0.5
Without prediction rho = 0.707
With prediction rho = 0.707
Without prediction rho = 0.95
With prediction rho = 0.95
Perfect CSI, roh = 1
0
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